In this work, we introduce and calibrate a computational model for fully three-dimensional simulations of cells in arbitrary flows.
Our approach uses a Lattice-Boltzmann solver for the fluid and a direct force formulation for the elastic equations.
In contrast to earlier works [1]}, [2]}, [3]}, [4]}, [5]} our model uses a three-parameter Mooney–Rivlin elastic energy functional.
To demonstrate the need for this more complex elastic model, we carry out extensive FluidFM® indentation experiments for REF52 (rat embryonic fibroblast) cells at large cell deformation up to \({80}{}\)  [6]}.

In addition, our model compares favorably with previous AFM experiments on bovine endothelial cells [1]} as well as artificial hydrogel particles [8]}.
Our model provides a much more realistic force–deformation behavior compared to the small-deformation Hertz approximation, but is still simple and fast enough to allow the simulation of dense cell suspensions in reasonable time.
Particularly, our approach is less computationally demanding than conventional finite-element methods which usually require large matrix operations. Furthermore, it is easily extensible and allows, e.g., the inclusion of a cell nucleus by the choice of different elastic moduli for different parts of the volume.
